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Theorem impl 380
Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
impl.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
impl (((𝜑𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem impl
StepHypRef Expression
1 impl.1 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
21expd 258 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32imp31 256 1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem is referenced by:  sbc2iedv  3047  csbie2t  3117  foco2  5767  erth  6593  distrlem1prl  7595  distrlem1pru  7596  uz11  9564  elpq  9662  divgcdcoprm0  12115  cncongr1  12117  prmpwdvds  12367  issgrpd  12837  dfgrp3mlem  12995  efltlemlt  14491
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