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Theorem ancom1s 651
Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypothesis
Ref Expression
an32s.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
ancom1s (((𝜓𝜑) ∧ 𝜒) → 𝜃)

Proof of Theorem ancom1s
StepHypRef Expression
1 pm3.22 460 . 2 ((𝜓𝜑) → (𝜑𝜓))
2 an32s.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 580 1 (((𝜓𝜑) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 206  df-an 397
This theorem is referenced by:  odi  8526  sornom  10213  leltadd  11639  divmul13  11858  absmax  15214  fzomaxdif  15228  dmatsgrp  21848  comppfsc  22883  iocopnst  24303  mumul  26530  lgsdir2  26678  branmfn  31047  chirredlem2  31333  chirredlem4  31335  icoreclin  35828  relowlssretop  35834  pibt2  35888  frinfm  36194  fzmul  36200  fdc  36204  rpnnen3  41342
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