Theorem anim12ii 559

Description: Conjoin antecedents and consequents in a deduction.

Hypotheses

Ref	Expression
anim12ii.1	|- (ph -> (ps -> ch))
anim12ii.2	|- (th -> (ps -> ta))

Assertion

Ref	Expression
anim12ii	|- ((ph /\ th) -> (ps -> (ch /\ ta)))

Proof of Theorem anim12ii

Step	Hyp	Ref	Expression
1		anim12ii.1	. . . 4 |- (ph -> (ps -> ch))
2	1	com12 11	. . 3 |- (ps -> (ph -> ch))
3		anim12ii.2	. . . 4 |- (th -> (ps -> ta))
4	3	com12 11	. . 3 |- (ps -> (th -> ta))
5	2, 4	anim12d 558	. 2 |- (ps -> ((ph /\ th) -> (ch /\ ta)))
6	5	com12 11	1 |- ((ph /\ th) -> (ps -> (ch /\ ta)))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  tz7.2 2931  funcnvuni 3564  eqfnfv 3797  fzoptht 6502  metelcls 7965

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