Theorem ad4antlr 499

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 497	. 2 |- ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) -> ps )
3	2	adantr 276	1 |- ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) -> ps )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  ad5antlr  501  ctm  7450  suplocexprlemub  8091  suplocexprlemlub  8092  maxabslemval  11991  xrmaxleim  12029  xrmaxiflemval  12035  fsumconst  12240  4sqlemsdc  13202