Theorem ancom1s 492

Description: Inference commuting a nested conjunction in antecedent.

Hypothesis

Ref	Expression
an1rs.1	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
ancom1s	|- (((ps /\ ph) /\ ch) -> th)

Proof of Theorem ancom1s

Step	Hyp	Ref	Expression
1		an1rs.1	. . . 4 |- (((ph /\ ps) /\ ch) -> th)
2	1	exp31 378	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com12 11	. 2 |- (ps -> (ph -> (ch -> th)))
4	3	imp31 362	1 |- (((ps /\ ph) /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  odi 4216  leltaddt 5658  rec11rt 5781  absmaxt 6897  climcmplem 7137  znnen 7503  bl2in 7840  htthlem11 8626  hmopcot 9943  branmfnt 10033  irredlem2 10313  irredlem4 10315

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain