Theorem mpidan 421

Description: A deduction which "stacks" a hypothesis. (Contributed by Stanislas Polu, 9-Mar-2020.) (Proof shortened by Wolf Lammen, 28-Mar-2021.)

Hypotheses

Ref	Expression
mpidan.1	|- ( ph -> ch )
mpidan.2	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Assertion

Ref	Expression
mpidan	|- ( ( ph /\ ps ) -> th )

Proof of Theorem mpidan

Step	Hyp	Ref	Expression
1		mpidan.1	. . 3 |- ( ph -> ch )
2	1	adantr 274	. 2 |- ( ( ph /\ ps ) -> ch )
3		mpidan.2	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	2, 3	mpdan 419	1 |- ( ( ph /\ ps ) -> th )

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:  sumrbdc  11342  prodrbdclem2  11536  tx2cn  13064  dvaddxxbr  13459  dvmulxxbr  13460