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Theorem exbidh 1943
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by NM, 26-May-1993.)
Hypotheses
Ref Expression
exbidh.1 (𝜑 → ∀𝑥𝜑)
exbidh.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exbidh (𝜑 → (∃𝑥𝜓 ↔ ∃𝑥𝜒))

Proof of Theorem exbidh
StepHypRef Expression
1 exbidh.1 . 2 (𝜑 → ∀𝑥𝜑)
2 exbidh.2 . . 3 (𝜑 → (𝜓𝜒))
32alexbii 1909 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 ↔ ∃𝑥𝜒))
41, 3syl 17 1 (𝜑 → (∃𝑥𝜓 ↔ ∃𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1630  wex 1853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-ex 1854
This theorem is referenced by:  exbidv  2000  exbid  2239  exbidOLD  2346  drex2  2469  ac6s6  34312
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