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Theorem syl2im 38
Description: Replace two antecedents. Implication-only version of syl2an 277. (Contributed by Wolf Lammen, 14-May-2013.)
Hypotheses
Ref Expression
syl2im.1 (𝜑𝜓)
syl2im.2 (𝜒𝜃)
syl2im.3 (𝜓 → (𝜃𝜏))
Assertion
Ref Expression
syl2im (𝜑 → (𝜒𝜏))

Proof of Theorem syl2im
StepHypRef Expression
1 syl2im.1 . 2 (𝜑𝜓)
2 syl2im.2 . . 3 (𝜒𝜃)
3 syl2im.3 . . 3 (𝜓 → (𝜃𝜏))
42, 3syl5 32 . 2 (𝜓 → (𝜒𝜏))
51, 4syl 14 1 (𝜑 → (𝜒𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  sylc  60  bi3ant  217  pm3.12dc  876  pm3.13dc  877  nfrimi  1434  vtoclr  4416  funopg  4962  xpiderm  6208  ixxssixx  8872  difelfzle  9094  bj-inf2vnlem1  10482
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