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Theorem ad2antlr 707
Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.) (Proof shortened by Wolf Lammen, 20-Nov-2012.)
Hypothesis
Ref Expression
ad2ant.1 (φψ)
Assertion
Ref Expression
ad2antlr (((χ φ) θ) → ψ)

Proof of Theorem ad2antlr
StepHypRef Expression
1 ad2ant.1 . . 3 (φψ)
21adantr 451 . 2 ((φ θ) → ψ)
32adantll 694 1 (((χ φ) θ) → ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  ad3antlr  711  simplr  731  simplrl  736  simplrr  737  ax11eq  2193  ax11el  2194  ltfinirr  4457  sfintfin  4532  caovord3  5631  nntccl  6170  sbthlem3  6205  nchoicelem17  6305
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