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Theorem rexeqi 2812
 Description: Equality inference for restricted existential qualifier. (Contributed by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
raleq1i.1 A = B
Assertion
Ref Expression
rexeqi (x A φx B φ)
Distinct variable groups:   x,A   x,B
Allowed substitution hint:   φ(x)

Proof of Theorem rexeqi
StepHypRef Expression
1 raleq1i.1 . 2 A = B
2 rexeq 2808 . 2 (A = B → (x A φx B φ))
31, 2ax-mp 8 1 (x A φx B φ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642  ∃wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620 This theorem is referenced by:  rexrab2  3004  rexprg  3776  rextpg  3778  opeq  4619  rexxp  4826  clos1basesucg  5884
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