Theorem ad4antlr 487

Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.)

Hypothesis

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

Assertion

Ref	Expression
ad4antlr	|- ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) -> ps )

Proof of Theorem ad4antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad3antlr 485	. 2 |- ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) -> ps )
3	2	adantr 274	1 |- ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) -> ps )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  ad5antlr  489  ctm  7074  suplocexprlemub  7664  suplocexprlemlub  7665  maxabslemval  11150  xrmaxleim  11185  xrmaxiflemval  11191  fsumconst  11395