MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rexbidvALT Structured version   Visualization version   GIF version

Theorem rexbidvALT 3035
Description: Alternate proof of rexbidv 3034, shorter but requires more axioms. (Contributed by NM, 20-Nov-1994.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rexbidv.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 1830 . 2 𝑥𝜑
2 rexbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2rexbid 3033 1 (𝜑 → (∃𝑥𝐴 𝜓 ↔ ∃𝑥𝐴 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wrex 2897
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701  df-rex 2902
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator