Theorem ad3antlr 477

Description: Deduction adding three conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.)

Hypothesis

Ref	Expression
ad2ant.1	|- ( ph -> ps )

Assertion

Ref	Expression
ad3antlr	|- ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) -> ps )

Proof of Theorem ad3antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad2antlr 473	. 2 |- ( ( ( ch /\ ph ) /\ th ) -> ps )
3	2	adantr 270	1 |- ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  ad4antlr  479  phpm  6400  phplem4on  6402  fidifsnen  6405  fisbth  6417  fin0  6419  fin0or  6420  prmuloc  6818  cauappcvgprlemopl  6898  cauappcvgprlemdisj  6903  cauappcvgprlemladdfl  6907  caucvgprlemopl  6921  axcaucvglemcau  7126  ssfzo12bi  9311  rebtwn2zlemstep  9339  btwnzge0  9382  addmodlteq  9480  frecuzrdgg  9498  cjap  9931  caucvgre  10005  minmax  10250  sumeq2d  10334  sumeq2  10335  bezoutlemmain  10531  dfgcd2  10547  lcmgcdlem  10603