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Theorem rexlimd2 2736
 Description: Version of rexlimd 2735 with deduction version of second hypothesis. (Contributed by NM, 21-Jul-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
rexlimd2.1 xφ
rexlimd2.2 (φ → Ⅎxχ)
rexlimd2.3 (φ → (x A → (ψχ)))
Assertion
Ref Expression
rexlimd2 (φ → (x A ψχ))

Proof of Theorem rexlimd2
StepHypRef Expression
1 rexlimd2.1 . . 3 xφ
2 rexlimd2.3 . . 3 (φ → (x A → (ψχ)))
31, 2ralrimi 2695 . 2 (φx A (ψχ))
4 rexlimd2.2 . . 3 (φ → Ⅎxχ)
5 r19.23t 2728 . . 3 (Ⅎxχ → (x A (ψχ) ↔ (x A ψχ)))
64, 5syl 15 . 2 (φ → (x A (ψχ) ↔ (x A ψχ)))
73, 6mpbid 201 1 (φ → (x A ψχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2614  ∃wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by: (None)
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