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Theorem sbft 2038
 Description: Substitution has no effect on a non-free variable. (Contributed by NM, 30-May-2009.) (Revised by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
sbft

Proof of Theorem sbft
StepHypRef Expression
1 sb1 1656 . . 3
2 simpr 447 . . . . 5
32ax-gen 1551 . . . 4
4 19.23t 1806 . . . 4
53, 4mpbii 202 . . 3
61, 5syl5 28 . 2
7 nfr 1767 . . 3
8 stdpc4 2037 . . 3
97, 8syl6 29 . 2
106, 9impbid 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1545  wex 1546  wnf 1549  wsb 1653 This theorem is referenced by:  sbf  2039  sbctt  3139 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1547  df-nf 1550  df-sb 1654
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