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Theorem syl2anr 274
Description: A double syllogism inference. (Contributed by NM, 17-Sep-2013.)
Hypotheses
Ref Expression
syl2an.1 (φψ)
syl2an.2 (τχ)
syl2an.3 ((ψ χ) → θ)
Assertion
Ref Expression
syl2anr ((τ φ) → θ)

Proof of Theorem syl2anr
StepHypRef Expression
1 syl2an.1 . . 3 (φψ)
2 syl2an.2 . . 3 (τχ)
3 syl2an.3 . . 3 ((ψ χ) → θ)
41, 2, 3syl2an 273 . 2 ((φ τ) → θ)
54ancoms 255 1 ((τ φ) → θ)
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-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  swopo  4017  opswapg  4734  coexg  4789  iotass  4811  resdif  5073  fvexg  5119  isotr  5381  xpexgALT  5683  addgt0sr  6521  axmulass  6567  axdistr  6568  negeu  6789
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