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Theorem max1ALT 10779
 Description: A number is less than or equal to the maximum of it and another. This version of max1 10778 omits the antecedent. Although it doesn't exploit undefined behavior, it is still considered poor style, and the use of max1 10778 is preferred. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by NM, 3-Apr-2005.)
Assertion
Ref Expression
max1ALT

Proof of Theorem max1ALT
StepHypRef Expression
1 leid 9174 . . 3
2 iffalse 3748 . . . 4
32breq2d 4227 . . 3
41, 3syl5ibrcom 215 . 2
5 id 21 . . 3
6 iftrue 3747 . . 3
75, 6breqtrrd 4241 . 2
84, 7pm2.61d2 155 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wcel 1726  cif 3741   class class class wbr 4215  cr 8994   cle 9126 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704  ax-resscn 9052  ax-pre-lttri 9069 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-nel 2604  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-er 6908  df-en 7113  df-dom 7114  df-sdom 7115  df-pnf 9127  df-mnf 9128  df-xr 9129  df-ltxr 9130  df-le 9131
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