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Theorem r19.29a 2448
 Description: A commonly used pattern based on r19.29 2444 (Contributed by Thierry Arnoux, 22-Nov-2017.)
Hypotheses
Ref Expression
r19.29a.1 (((φ x A) ψ) → χ)
r19.29a.2 (φx A ψ)
Assertion
Ref Expression
r19.29a (φχ)
Distinct variable groups:   χ,x   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.29a
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 r19.29a.1 . 2 (((φ x A) ψ) → χ)
3 r19.29a.2 . 2 (φx A ψ)
41, 2, 3r19.29af 2447 1 (φχ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ wcel 1390  ∃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-17 1416  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-ral 2305  df-rex 2306 This theorem is referenced by:  cnegexlem3  6965  cnegex  6966
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