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Theorem jcai 294
Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jcai.1 (φψ)
jcai.2 (φ → (ψχ))
Assertion
Ref Expression
jcai (φ → (ψ χ))

Proof of Theorem jcai
StepHypRef Expression
1 jcai.1 . 2 (φψ)
2 jcai.2 . . 3 (φ → (ψχ))
31, 2mpd 13 . 2 (φχ)
41, 3jca 290 1 (φ → (ψ χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101
This theorem is referenced by:  reu6  2707  f1ocnv2d  5627
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