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Theorem r19.35-1 2454
Description: Restricted quantifier version of 19.35-1 1512. (Contributed by Jim Kingdon, 4-Jun-2018.)
Assertion
Ref Expression
r19.35-1 (x A (φψ) → (x A φx A ψ))

Proof of Theorem r19.35-1
StepHypRef Expression
1 r19.29 2444 . . 3 ((x A φ x A (φψ)) → x A (φ (φψ)))
2 pm3.35 329 . . . 4 ((φ (φψ)) → ψ)
32reximi 2410 . . 3 (x A (φ (φψ)) → x A ψ)
41, 3syl 14 . 2 ((x A φ x A (φψ)) → x A ψ)
54expcom 109 1 (x A (φψ) → (x A φx A ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wral 2300  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-ral 2305  df-rex 2306
This theorem is referenced by:  r19.36av  2455  r19.37  2456  iinexgm  3899  bndndx  7936
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