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Theorem rexcom4a 2879
 Description: Specialized existential commutation lemma. (Contributed by Jeff Madsen, 1-Jun-2011.)
Assertion
Ref Expression
rexcom4a (xy A (φ ψ) ↔ y A (φ xψ))
Distinct variable groups:   x,A   x,y   φ,x
Allowed substitution hints:   φ(y)   ψ(x,y)   A(y)

Proof of Theorem rexcom4a
StepHypRef Expression
1 rexcom4 2878 . 2 (y A x(φ ψ) ↔ xy A (φ ψ))
2 19.42v 1905 . . 3 (x(φ ψ) ↔ (φ xψ))
32rexbii 2639 . 2 (y A x(φ ψ) ↔ y A (φ xψ))
41, 3bitr3i 242 1 (xy A (φ ψ) ↔ y A (φ xψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541  ∃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-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861 This theorem is referenced by:  rexcom4b  2880
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