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Theorem rexbidvALT 3318
Description: Alternate proof of rexbidv 3294, shorter but requires more axioms. (Contributed by NM, 20-Nov-1994.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rexbidvALT.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
rexbidvALT (𝜑 → (∃𝑥𝐴 𝜓 ↔ ∃𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem rexbidvALT
StepHypRef Expression
1 nfv 1906 . 2 𝑥𝜑
2 rexbidvALT.1 . 2 (𝜑 → (𝜓𝜒))
31, 2rexbid 3317 1 (𝜑 → (∃𝑥𝐴 𝜓 ↔ ∃𝑥𝐴 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wrex 3136
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-nf 1776  df-rex 3141
This theorem is referenced by: (None)
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