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Theorem ispcon 24912
 Description: The property of being a path-connected topological space. (Contributed by Mario Carneiro, 11-Feb-2015.)
Hypothesis
Ref Expression
ispcon.1
Assertion
Ref Expression
ispcon PCon
Distinct variable groups:   ,,,   ,,
Allowed substitution hint:   ()

Proof of Theorem ispcon
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 unieq 4026 . . . 4
2 ispcon.1 . . . 4
31, 2syl6eqr 2488 . . 3
4 oveq2 6091 . . . . 5
54rexeqdv 2913 . . . 4
63, 5raleqbidv 2918 . . 3
73, 6raleqbidv 2918 . 2
8 df-pcon 24910 . 2 PCon
97, 8elrab2 3096 1 PCon
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708  cuni 4017  cfv 5456  (class class class)co 6083  cc0 8992  c1 8993  ctop 16960   ccn 17290  cii 18907  PConcpcon 24908 This theorem is referenced by:  pconcn  24913  pcontop  24914  cnpcon  24919  txpcon  24921  ptpcon  24922  indispcon  24923  conpcon  24924  cvxpcon  24931 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-pcon 24910
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