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Theorem simplbi2com 1374
Description: A deduction eliminating a conjunct, similar to simplbi2 377. (Contributed by Alan Sare, 22-Jul-2012.) (Proof shortened by Wolf Lammen, 10-Nov-2012.)
Hypothesis
Ref Expression
simplbi2com.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
simplbi2com (𝜒 → (𝜓𝜑))

Proof of Theorem simplbi2com
StepHypRef Expression
1 simplbi2com.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21simplbi2 377 . 2 (𝜓 → (𝜒𝜑))
32com12 30 1 (𝜒 → (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mo2r  1994  mo3h  1995  elres  4668  xpidtr  4739  peano5nnnn  7109  peano5nni  8098
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