Theorem ad5antlr 771

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

Hypothesis

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

Assertion

Ref	Expression
ad5antlr	|- ( ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Proof of Theorem ad5antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- ( ph -> ps )
2	1	ad4antlr 769	. 2 |- ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) -> ps )
3	2	adantr 481	1 |- ( ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  ad6antlr  773  restmetu  22375  foresf1o  29343  fimaproj  29900  locfinreflem  29907  pstmxmet  29940  mblfinlem3  33448  itg2gt0cn  33465  pell1234qrmulcl  37419  suplesup  39555  limclner  39883  bgoldbtbnd  41697